Influence of defect phonon modes on hopping conduction

Abstract

The hopping-conduction formalism developed in part I is used to study the effect on the jump rate of defect phonon modes. Numerical results are displayed for a wide range of parameters. An important observation is the confirmation, for a certain range of parameters, of an inherent T ^1/4-law dependence of the jump rate as previously reported by other workers. It is found that with modified in-band phonon modes the T ^1/4 law is still observed, although the jump rate itself may be changed by several orders of magnitude. The constant T ₀ appearing in the T ^1/4 law changes by comparatively little, however. Local phonon modes, on the other hand, tend to destroy the T ^1/4 law as well as stabilizing an activated form of the hopping rate. The calculations are related to experimental data on Ge, Si and GaAs, and it is shown that certain difficulties which arise in a variable-range-hopping interpretation of the data can be resolved. Difficulties exist in the case of carbon, which may point the direction of further study.